David Cameron raised the prospect of clawing back powers from Brussels as tensions continued to grow within the Coalition over Britain's relationship with the European Union.

The Deputy Prime Minister, Nick Clegg, condemned any "tampering" with the UK's membership terms and warned Tory Eurosceptics that it would be "economic suicide" for the country to retreat to the continent's margins.

Mr Cameron wants to placate growing demands among his own MPs – 81 of whom defied a three-line whip last week to demand a referendum on Europe – for a fundamental rethink of Britain's position within the EU. He has already promised a Whitehall review of the country's membership terms and yesterday hinted an attempt could be launched within the next year to repatriate some powers.

Mr Cameron suggested it could be made during the expected move by the 17 eurozone members to amend the EU's constitution to bind themselves more closely together. "If they do that, there may well be opportunities for Britain to further our national interest in some way and we would examine that as a coalition government," he told BBC1's Andrew Marr Show.

Mr Cameron added that he was "looking for other ways to further our national interest in Europe".

But he said that the Liberal Democrats could limit the extent of any shift of powers: "I would like to see further rebalancing but we are obviously going to have to act as a coalition."

MPs will get a new opportunity to step up their criticism of Brussels next Tuesday when the Commons debates plans to increase the EU's budget between 2014 and 2020. The Government intends to table a motion welcoming ministers' efforts to limit the increase, but Conservative MPs are expected to rally behind a more strongly worded amendment, calling for action to resist the planned rise.

Mr Clegg delivered a sharp rebuke to Tory Eurosceptics yesterday as he argued that tampering with the EU's founding texts would leave the continent economically paralysed. He warned: "Being shoved to the margins, or retreating there voluntarily, would be economic suicide: a surefire way to hurt British businesses and lose jobs."

Douglas Alexander, the shadow Foreign Secretary, said: "There does need to be change in Europe. But it doesn't help the case for reform when you have got a Prime Minister and a leader of the Liberal Democrats in such obvious disagreement on so basic an issue."